WELCOME all to our lecture on kinematics, a branch of physics which relates to an algebraic calculation of geometry in motion.As such, kinematics is taken as a geometry of motion.
It focuses on calculating the movement of a particular body such as a particle, a part of a machinery or even the movement of a galactic body like a star or a planet.
Application of algebra, mathematics of functions for a cartesian coordinate and matrices are involved to calculate motion in dimensions as linear, translational and rotations.
It brings to point two dimensional as well as three dimensional points of movements by a particular travelling body such as a projectile.
A coordinate system such as a point from a starting point taken as zero (0) and down south to be a negative point seventy (-70) are two coordinate points and from that southern point with a stationary structure with point zero (0) or a structure such as a tower with its height (30) is the third coordinate point.
With such a picture in mind, and with the fixed coordinate points of the X and Y axes, a particle or a projectile can move with that as the frame of reference.
In the above scenario, quantities such as speed, velocity and acceleration can be calculated.
Speed is the rate of movement of a body or the particle’s movement per unit time.
Changes in the speed create the second path for its movement and that is the average speed or displacement.
That is the curvature whose tangent will mark its velocity as a derivative.
That is, velocity results from the average size of speed from the original speed with that of the second size or magnitude of the speed.
The acceleration is obtained in a similar way to the first derivative that is the average speed.
Specifically, the average of the velocities from the initial and the final velocities give the magnitude of acceleration as the second derivative.
From the vector diagrams considering several factors of accelerations such as the Coriolis Effect, centripetal and radial accelerations taken into account.
In any kinematic calculation, the frame of reference is always very important, without which the movement of the body will not be properly calculated.
Such is applied in a linear, two-dimensional calculation such as a mechanical system with a rigid transformation.
A rigid transformation would be the Euclidean Geometry whereby it involves a straight-line path of a motion of the body or projectile.
The circular path taken by a traveling particle involves the calculations involving the rotational geometry with polar coordinates.
It involves the sine and the cosine functions to determine the path of the travelling particle or body. That is a two-dimensional path marked by a point, a line from the centre and another line closing in the angle subtended for that rotation.
The velocity and the acceleration for such motions are tangential to the orbit.
Therefore, velocity and acceleration are not obtained from any inward points of the rotation.
Speed is a scalar quantity because it does not have a direction of travel. It only has the size or magnitude of travel.
The next quantity after speed is the velocity that accounts for any changes in the rate of speed.
Both of these two quantities are calculated with reference to time.
Time is factored as a very important variable because it determines the derivative of the average speed.
Velocity is the first derivative of speed.
It represents the values of changes in speed.
The third is the acceleration as the second derivative of the particle or body in motion.
A body can accelerate or decelerate, just like changing speed from a low speed to high speed or vice versa.
Appropriate signs as a plus or minus to indicate an acceleration and a deceleration respectively or wording can be made if it is acceleration or deceleration just like an increase or a decrease in speed.
There can also be uniform (constant) speed, velocity and acceleration.
An important idea is to pictorially show the motion of the body or projectile on a graph.
It is always advisable to have a title for any graph that is drawn in kinematics.
The frame of reference in the X and Y axis are to be correctly labelled with the correct variables.
In the X axis, it is always the independent variable that is labelled.
Example in the case of kinematics would be the time in any unit.
It can be time in hours, minutes, seconds or even years.
These are variables that cannot be changed.
The other coordinate is the y axis which always is labelled with the dependent variable (s).
In the case of this subject it will be either, distance, displacement, speed, velocity or acceleration.
These are variables that can be changed.
Having plotted a graph, would enable one to see the inclination of the particle and locate correctly where the travelling body be in X time.
It will also help to give the magnitude and the direction of the speed as it is a vector quantity.
The astronomical calculations of the movement of the planetary bodies, or other interstellar bodies, are perfected with the use of kinematics.
Kinetics is another field of study that is concerned with motion but specifically looks at how the motion of bodies of particles are derived.
There are mathematical algebraic formulas to work out the derivatives of the body as speed, velocity and acceleration.
A fourth factor is that each derivative can be identified as a function of time.
In rotational and translational calculations done in matrices, the independent variable of time is calculated alongside the derivatives of the travelling body under study.
My prayer for PNG today is “Come to me, with all your hearts, don’t let fear keep us apart. Long have I waited for your coming home to me and living, deeply a new life,” says the Lord.
Next week: Dynamics (force and motion)
- Michael Uglo is the author of the science textbook Science in PNG, Pacific, Asia & Caribbean, and a lecturer in avionics, auto-piloting and aircraft engineering. Please send comments to: [email protected]